4753
J. Phys. Chem. 1988,92,4753-4758
Theory of Differential Line Broadening in Coupled Spin Systems in Macromolecules and Molecular Aggregates. Applications to the Study of Micellar Systems Lian-Pin Hwang,* Pei-kin Wang, Department of Chemistry, National Taiwan University, Taipei, Taiwan, ROC, and Institute of Atomic and Molecular Science, Academia Sinica, Nankang, Taipei, Taiwan, ROC
and Tuck C. Wong* Department of Chemistry, University of Missouri, Columbia, Missouri 6521 1 (Received: July 9, 1987; In Final Form: February 19, 1988)
The theory of differential line broadening (DLB) in spin-coupled multiplets in molecular systems where there is a slow isotropic overall reorientation and a fast internal motion has been derived on the basis of the solution of the stochastic Liouville equation. The most prominent example is the proton-coupled methyl 13Cmultiplet. From the line-width differences between various components of the multiplet, the correlation time for the slow overall reorientation and the chemical shift anisotropy can be determined. Applications to the study of the molecular dynamics of the sodium deoxycholate/water micellar system and a viscoelastic micellar system are illustrated. The results show that the DLB effect is a useful tool complementary to multifield relaxation time and nuclear Overhauser effect studies in the investigation of molecular dynamics.
Introduction Differential line broadening (DLB) of nuclear magnetic resonance (NMR) lines in coupled spin 1/2-spin systems was first discussed by Shimizu many years ago.' The difference in the spin-spin relaxation times of different components in the multiplet can be attributed to the interference between the dipole-dipole (DD) and the chemical shift anisotropy (CSA) relaxation mechanisms. Such effects has since been observed in 19F-'H system,2 in 31P-19Esystem^,^,^ in 15N-'H system^,^ in I3C-lH in a 31P-1H system,8 and in a 'H-lH ~ y s t e m . ~A detailed review of relaxation in coupled spin systems has been presented by Vold and Vold.Io Farrar et al? have recently outlined the conditions under which the DLB effect is likely to be observed. Recently, the DLB effect in proton-coupled methyl I3C multiplets in two types of systems-niicellar aggregates and methyl I3C-enriched transfer RNA-has been observed in our laboratory." In both of these systems, the dynamics of the molecules has to be described by more than one motion. Frequently, a model '1) overall isotropic molecular (or that consists of a slow ( o o T c 2 aggregate) reorientation and a fast (woTc
